Electronic and micromechanical devices are formed by patterning successive layers on a substrate using lithography. The patterns are formed by applying a layer of photoresist to a surface. Light is then passed through a patterned imaging plate, such as a mask or reticle, to expose the photoresist in patterns that correspond to the desired features on the substrate. A developer is applied and the photoresist is etched away leaving only the features in a pattern corresponding to the pattern on the mask. As the size of the features, such as parts of transistors, decreases, there are more features on the same size mask and the mask designs becomes more complex.
For very small features, phase shift technology (referred to as phase shift masks) is used. In a conventional non-phase shift mask, the light transmitted through adjacent transparent areas of the mask is in phase and the features are large enough that the phase of the light does not significantly affect the amount of light that hits the photoresist. Each transparent area on the mask results in a corresponding exposed area on the photoresist. With very small features, that is when the dimensions of the features are close to the wavelength of the light, diffraction occurs as the light passes through the mask. The light passing through adjacent transparent areas will interfere constructively or destructively, so that in some places on the photoresist the amplitude of the light adds together and on some places of the photoresist that light will cancel itself out. The resulting pattern on the photoresist ends up different from the pattern on the mask.
In a phase shift mask, light transmitted through adjacent features is phase shifted by the mask so that constructive and destructive interference is intentionally used to form the pattern on the photoresist. The mask is a grid of pixels that either block light, transmit light, or transmit light with a phase shift. The intentional use of optical interference gives greater control over the creation of small features. However it makes mask design more complex.
Masks are designed using computer software. For complex mask designs (e.g., the designs of phase shift masks for sub-wavelength features), accurate mask design software is very complex and the calculations may be very slow. As a result, approximations and simplifications are used to estimate the pattern that will be created by a particular mask. The thin mask method uses geometrical optics to calculate the electric field transmitted by light passing through the mask onto the photoresist. The thin mask method ignores light scattering effects due to the shape of particular mask features. There is more than one approach to effectively add thick mask effects to the thin mask method. A boundary layer method modifies the thin mask field in feature edge areas (the so-called boundary layer) to account for some scattering effects. The edge domain decomposition method adds edge scattering corrections to the thin mask field to improve the accuracy. Other methods are also used.
However, actual masks are not thin. Accurately accounting for the effects of the thickness of the mask becomes more important as features become smaller and can allow the mask design to be corrected for increasingly strong scattering effects and aggressive illumination schemes.